# Scattering on plane waves and the double copy

## TL;DR

This paper extends the double copy relationship between gravity and gauge theory scattering amplitudes from flat space to curved plane wave backgrounds, revealing a non-local replacement rule and memory effects.

## Contribution

It demonstrates that the double copy principle applies to gravitational plane wave backgrounds, including non-local background field replacements and tail terms.

## Key findings

- Graviton amplitudes on gravitational plane waves are the double copy of gluon amplitudes on gauge plane waves.
- A non-local replacement rule for background fields and momenta is required.
- Memory effects in scattering amplitudes also double copy, indicating a deeper structure.

## Abstract

Perturbatively around flat space, the scattering amplitudes of gravity are related to those of Yang-Mills by colour-kinematic duality, under which gravitational amplitudes are obtained as the 'double copy' of the corresponding gauge theory amplitudes. We consider the question of how to extend this relationship to curved scattering backgrounds, focusing on certain 'sandwich' plane waves. We calculate the 3-point amplitudes on these backgrounds and find that a notion of double copy remains in the presence of background curvature: graviton amplitudes on a gravitational plane wave are the double copy of gluon amplitudes on a gauge field plane wave. This is non-trivial in that it requires a non-local replacement rule for the background fields and the momenta and polarization vectors of the fields scattering on the backgrounds. It must also account for new 'tail' terms arising from scattering off the background. These encode a memory effect in the scattering amplitudes, which naturally double copies as well.